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Find the volume of a right circular cone that has a height of 13.8 m and a base with a
circumference of 15.8 m. Round your answer to the nearest tenth of a cubic meter.
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Verified Answer :

GinnyAnswer

To find the volume of a right circular cone with a height of 13.8 meters and a base circumference of 15.8 meters, we'll go through a few steps:

Step 1: Determine the radius of the base of the cone.
The formula for the circumference (\(\( C \)\)) of a circle is:
\(\[ C = 2\pi r \]\)
where \(\( r \)\) is the radius of the circle, and \(\( \pi \)\) is approximately \(\( 3.14159 \)\).

Given the circumference of the base is 15.8 meters, we can solve for \(\( r \)\):
\(\[ r = \frac{C}{2\pi} \]\)
\(\[ r = \frac{15.8}{2\pi} \]\)
\(\[ r \approx 2.5146481008519466 \text{ meters} \]\)

Step 2: Calculate the volume of the cone.
The formula for the volume (\(\( V \)\)) of a cone is:
\(\[ V = \frac{1}{3}\pi r^2 h \]\)
where \(\( h \)\) is the height of the cone.

Plugging the values we have:
\(\[ V = \frac{1}{3}\pi (2.5146481008519466)^2 \times 13.8 \]\)
\(\[ V \approx 91.38231198495974 \text{ cubic meters} \]\)

Step 3: Round the volume to the nearest tenth.
The volume to the nearest tenth of a cubic meter is approximately \(\( 91.4 \)\) cubic meters.

So the volume of the right circular cone with a height of 13.8 meters and a base circumference of 15.8 meters, rounded to the nearest tenth, is \(\( 91.4 \)\) cubic meters.

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